Q8 of 249 Page 32

If A and B are two independent events such that =2/15 and =1/6, then find P(B).

Let , denote the complements of A, B respectively.


Given that, P(A∩) )


P(A)P()


P(A)[1–P(B)]


P(A)=1/6[1–P(B)]


P(A'∩B)


P(A')P(B)


[1–P(A)]P(B) )


[1–1/6{1–P(B)}]P(B) )


[{6–6P(B)–1}/{6–6P(B)}]P(B) )


15[5–6P(B)]P(B)=2[6–6P(B)]


15[5–6P(B)]P(B)=12[1–P(B)]


5[5–6P(B)]P(B)=4[1–P(B)]


25P(B)–30[P(B)]2=4–4P(B)


–30[P(B)]2+25P(B)+4P(B)–4=0


30[P(B)]2–29P(B)+4=0


30a2–29a+4=0 where P(B)=a


30a2–24a–5a+4=0


6a(5a–4)–1(5a–4)=0


(6a–1)(5a–4)=0


6a–1=0


6a=1


a


P(B)


5a–4=0


5a=4


a=


P(B)


Therefore, P(B),


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Given two independent events A and B such that P (A)=0.3 and P(B) = 0.6 Find

i. P (A B)


ii.


iv.


iv. P (A ∪ B)


v. P (A / B)


vi. P (B / A)

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A and B are two independent events. The probability that A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of occurrence of two events.

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